Answer is A.
i) n^2-1 is odd
This tells you that n is even, because if it were odd, its square would be odd too (odd*odd=odd) and n^2-1 would be even.
Sufficient.
ii) Root of n is integer
This doesn't tell you if n is even. For example, Root of 9 is 3 (an integer), Root of 4 is 2 (an integer) as well.
Insufficient
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